Pandora Hearts has a character sort of like that, but the manga is not focused on them.
http://www.mangago.zone/read-manga/three_days_of_happiness/
I think this one fits pretty well! The MC is a loser in life, sells a fat chunk of his lifespan with only a few months left. Uh, hardly anyone knows besides the people involved in the transaction, since people would think he's a loon if he goes on about selling some of his years. He doesn't really know what to do in the beginning but he steadily changes and lives happily and carefreely in his last days ヾ(❀╹◡╹)ﾉ~
Toki doki (one shot) ٩(๑❛ᴗ❛๑)۶
http://www.mangago.zone/read-manga/toki_doki/ is a really good oneshot that fits !
I'm curious if there are any manga similar to "Your Lie in April" where the main lead(s) have their days numbered; but doesn't inform the anyone else about it. I love the idea where they make the best out of their last days and slowly uplifting others during the process. Thank you! (& Merry Christmas)